"At the very least the premier should meet with the young Kamilaroi woman Cheree Toka," Mr Foley said in a statement.

"Flying the flag of our First Peoples alongside the national flag on NSW's most famous landmark will be a unifying gesture."

Mr Foley's pledge to fly the flag 365 days a year sparked an angry backlash from parts of the community last week with Sydney broadcaster Alan Jones saying the Labor leader had dug his political grave.

"Why is Mr Foley representing the concerns of the piddling minority?" Mr Jones said in a tweet.

Ms Berejiklian on Wednesday noted it was a Liberal government which introduced flying the flag on the bridge 15 days a year.

But former Liberal premier Barry O'Farrell, who was at the helm when the decision was made in 2013, has come out in support of Mr Foley's plan.

"The idea of extending it throughout the year is a reasonable & sensible idea," Mr O'Farrell tweeted.